I think it does depend on the genre . In pop music the composer isn't really so important because the song itself usually isn't as important as the performer .

That Freddie and the Dreamers song , I'm in Love with you... the song Bits and Pieces by the Dave Clarke Five. In either case I doubt if the composer would care so long as he was getting the royalties .

I read an interview with the man who set up the Eden Project in Cornwall   - I don't remember his name   .He said that he had financed the project from the royalties from a very successful song he had written sometime in the seventies , but declined to name the song saying that he was far too embarrassed .